Finite Group Databasebeta

← #34060875

Subgroups — #34060875

Order 19072.

276 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750584C211yesmaximal, characteristic
2#23750569C211yesmaximal, characteristic
3#23750498C214yesmaximal
4C4⋊Q8×D149C211yesmaximal, characteristic
5C2×D149⋊C8C2212yes—
6C2×C4⋊#10597010C2212yes—
7#18011966—21no—
8#18011966—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4—21no—
11C2×Q8×D149—21no—
12#18011911C411yescharacteristic, complemented
13#18011910—21no—
14#18011910C412yescomplemented
15#18011909—21no—
16C4⋊C4×D149—21no—
17C4⋊C4×D149C2212yes—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21D149⋊C8—22no—
22D149⋊C8Q814yescomplemented
23C2×#11924753—22no—
24C4⋊#10597010—24no—
25C2×Dic298—22no—
26C2×Dic298—21no—
27Q8×D149—44no—
28C2×C4×D149—22no—
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149C2311yescharacteristic
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C412yes—
34#14558715—22no—
35#14558715—22no—
36C4×Dic149C2×C411yescharacteristic
37C4×Dic149D411yescharacteristic
38C4×Dic149D411yescharacteristic
39C2×Q8×C149—21no—
40C4⋊C4×C149—21no—
41C4⋊C4×C149C2×C412yes—
42C42×C149C2×C411yescharacteristic
43C2×#10597010—42no—
44C2×#10597010—42no—
45C2×#10597010—42no—
46#11924753—24no—
47C22×D149C2×D411yescharacteristic
48Dic298—44no—
49Dic298—42no—
50C2×Dic149—22no—
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149C22⋊C411yescharacteristic
53C2×Dic149C2×D411yescharacteristic
54C4×D149—22no—
55C4×D149—22no—
56C4×D149—44no—
57C4×D149C2×Q812yes—
58C4×D149#4112yes—
59Q8×C149—42no—
60C2×C4×C149—22no—
61C2×C4×C149C22⋊C411yescharacteristic
62C2×C4×C149C22⋊C411yescharacteristic
63C2×C4×C149C22×C411yescharacteristic
64C22×C149C2×C22⋊C411yescharacteristic
65C2×D149#12411yescharacteristic
66C2×D149C4⋊Q811yescharacteristic
67C2×D149AGL(1,ℤ/8)12yes—
68C2×D149#13712yes—
69#10597010—82no—
70C4×C149—21no—
71C4×C149—21no—
72C4×C149—42no—
73C4×C149C4×Q812yes—
74Dic149—21no—
75Dic149—21no—
76Dic149—42no—
77Dic149C22⋊Q812yes—
78C2×C149#39111yescharacteristic
79C2×C149#41811yescharacteristic
80C2×C149#41911yescharacteristic
81D149#48912yes—
82D149#50112yes—
83C149#199311yescharacteristic, complemented, Sylow
84#1993—1491nomaximal, Sylow
85C2×C4⋊Q8—1491no—
86C2×#97—1491no—
87#382—1491no—
88#340—1494no—
89C22×Q8—2981no—
90C22×C8—1492no—
91C4⋊Q8—2981no—
92C4⋊Q8—2981no—
93C4⋊Q8—1492no—
94C4⋊Q8—1491no—
95C4⋊Q8#1059701011yescharacteristic, complemented
96C2×C4⋊C4—2981no—
97C2×C4⋊C4—1492no—
98C2×C4⋊C4—1492no—
99C2×C42—1491no—
100#97—2981no—
101#97—2981no—
102#95—2981no—
103#95—2981no—
104C2×Q8—21no—
105C2×Q8—2982no—
106C2×Q8—2981no—
107C2×Q8—5964no—
108C22×C4—2982no—
109C22×C4—2982no—
110C22×C4—1491no—
111C22×C4—1491no—
112C22×C4—1491no—
113C2×C8—2982no—
114C2×C8—2982no—
115C2×C8—1494no—
116C4⋊C4—21no—
117C4⋊C4—2982no—
118C4⋊C4—2982no—
119C4⋊C4—2981no—
120C4⋊C4—2984no—
121C4⋊C4—1492no—
122C4⋊C4C2×#1059701012yes—
123C42—1491no—
124C42—1491no—
125C42—1491no—
126C42C2×#1059701011yescharacteristic
127C23—1491no—
128Q8—42no—
129Q8—5962no—
130Q8—5964no—
131C2×C4—22no—
132C2×C4—2982no—
133C2×C4—2982no—
134C2×C4—2982no—
135C2×C4—5964no—
136C2×C4—5962no—
137C2×C4—5962no—
138C2×C4—5962no—
139C2×C4—1491no—
140C2×C4—1491no—
141C2×C4—1491no—
142C2×C4—1492no—
143C2×C4—1492no—
144C2×C4C22⋊#1059701011yescharacteristic
145C2×C4C22⋊#1059701011yescharacteristic
146C2×C4C22×#1059701011yescharacteristic
147C8—2984no—
148C22—1491no—
149C22—1491no—
150C22—1492no—
151C22—1492no—
152C22C2×C22⋊#1059701011yescharacteristic
153C4—21no—
154C4—21no—
155C4—42no—
156C4—2981no—
157C4—2981no—
158C4—5962no—
159C4—1492no—
160C4—11922no—
161C4Q8×#1059701012yes—
162C2—1492no—
163C2—1492no—
164C2(C2×#10597010)⋊Q811yescharacteristic
165C2#2375061711yescharacteristic
166C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1993
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
12. #18011911C4semidirect
14. #18011910C4semidirect
19. C4⋊Q8×C149C4semidirect
22. D149⋊C8Q8semidirect
83. C149#1993semidirect
95. C4⋊Q8#10597010semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237505842
#237505692
#237504982
C4⋊Q8×D1492
#1993149